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arXiv · 2204.01255

Cartan $F(R)$ Gravity and Equivalent Scalar-Tensor Theory

Tomohiro Inagaki·Masahiko Taniguchi
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Abstract

We investigate the Cartan formalism in $F(R)$ gravity. $F(R)$ gravity has been introduced as a theory to explain cosmological accelerated expansion by replacing the Ricci scalar $R$ in the Einstein-Hilbert action with a function of $R$. As is well-known, $F(R)$ gravity is rewritten as a scalar-tensor theory by using the conformal transformation. Cartan $F(R)$ gravity is described based on the Riemann-Cartan geometry formulated by the vierbein. In the Cartan formalism, the Ricci scalar $R$ is divided into two parts, one derived from the Levi-Civita connection and the other from the torsion. Assuming the spin connection independent matter action, we have successfully rewritten the action of Cartan $F(R)$ gravity into the Einstein-Hilbert action and a scalar field with canonical kinetic and potential terms without any conformal transformations. The resulting scalar-tensor theory is useful in applying the usual slow-roll scenario. As a simple case, we employ the Starobinsky model and evaluate fluctuations in the cosmological microwave background radiation.

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Tomohiro Inagaki, Masahiko Taniguchi. 2022-04-04. Cartan $F(R)$ Gravity and Equivalent Scalar-Tensor Theory. https://doi.org/10.3390/sym14091830

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